How to calculate the 95% confidence interval for the slope in a linear regression model in R

Question

Here is an exercise from Introductory Statistics with R:

With the rmr data set, plot metabolic rate versus body weight. Fit a linear regression model to the relation. According to the fitted model, what is the predicted metabolic rate for a body weight of 70 kg? Give a 95% confidence interval for the slope of the line.

rmr data set is in the 'ISwR' package. It looks like this:

> rmr    body.weight metabolic.rate 1         49.9           1079 2         50.8           1146 3         51.8           1115 4         52.6           1161 5         57.6           1325 6         61.4           1351 7         62.3           1402 8         64.9           1365 9         43.1            870 10        48.1           1372 11        52.2           1132 12        53.5           1172 13        55.0           1034 14        55.0           1155 15        56.0           1392 16        57.8           1090 17        59.0            982 18        59.0           1178 19        59.2           1342 20        59.5           1027 21        60.0           1316 22        62.1           1574 23        64.9           1526 24        66.0           1268 25        66.4           1205 26        72.8           1382 27        74.8           1273 28        77.1           1439 29        82.0           1536 30        82.0           1151 31        83.4           1248 32        86.2           1466 33        88.6           1323 34        89.3           1300 35        91.6           1519 36        99.8           1639 37       103.0           1382 38       104.5           1414 39       107.7           1473 40       110.2           2074 41       122.0           1777 42       123.1           1640 43       125.2           1630 44       143.3           1708 

I know how to calculate the predicted y at a given x but how can I calculate the confidence interval for the slope?

Answer 1

Let's fit the model:

> library(ISwR) > fit <- lm(metabolic.rate ~ body.weight, rmr) > summary(fit)  Call: lm(formula = metabolic.rate ~ body.weight, data = rmr)  Residuals:     Min      1Q  Median      3Q     Max  -245.74 -113.99  -32.05  104.96  484.81   Coefficients:             Estimate Std. Error t value Pr(>|t|)     (Intercept) 811.2267    76.9755  10.539 2.29e-13 *** body.weight   7.0595     0.9776   7.221 7.03e-09 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 157.9 on 42 degrees of freedom Multiple R-squared: 0.5539, Adjusted R-squared: 0.5433  F-statistic: 52.15 on 1 and 42 DF,  p-value: 7.025e-09  

The 95% confidence interval for the slope is the estimated coefficient (7.0595) ± two standard errors (0.9776).

This can be computed using confint:

> confint(fit, 'body.weight', level=0.95)                2.5 % 97.5 % body.weight 5.086656 9.0324